Permeability (commonly symbolized as k) is a measure of the ability of a material to transmit fluids, which is of great importance in determining the dynamic flow characteristics of hydrocarbons in oil and gas reservoirs. Typically, permeability of an earth formation may be characterized as horizontal permeability (kh) and vertical permeability (kv), which measure the permeability in the horizontal and vertical planes, respectively. Earth formations are complex and heterogeneous such that permeability is not distributed uniformly. Interval Pressure Transient Test (IPTT) with a modular dynamic tester have proved to be an efficient means for characterizing permeability distribution near a wellbore of a reservoir, and IPTT is widely accepted as a preferred approach for layered earth formation systems.
An IPTT requires a dual-probe or a dual-packer module and at least one vertical observation probe positioned below or above either the dual-probe or the dual-packer module to obtain the formation testing data. Typically, multiple sets of probes and packers (modules) are involved in the testing, and each set of probe(s) and packer(s) is referred to as a “test station”.
Two approaches are used to interpret IPTT data: analytical method and numerical method. For example, Goode and Thambynayagam (Analytic Models for a Multiple Probe Formation Tester,” SPE 20737 presented at the Annual Technical Conference and Exhibition of the SPE, New Orleans, 1990), Kuchuk (Pressure Behavior of the MDT Packer Module and DST in Crossflow-Multilayer Reservoirs, JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING (1994) 11, 123), and Onur et al. (Pressure-Transient Analysis of Dual Packer-Probe Wireline Formation Testers in Slanted Wells, SPE 90250 presented at the SPE Annual Technical Conference and Exhibition, Houston, September 2004) disclosed analytical methods for IPTT interpretation. Jackson et al. (An Integrated Approach to Interval Pressure Transient Test Analysis Using Analytical and Numerical Methods, SPE 81515 presented at the SPE 13th Middle East Oil Show & Conference, Bahrain, Apr. 2003) and Xian et al. (An Integrated Efficient Approach To Perform IPTT Interpretation, SPE 88561 presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Perth, Australia, October, 2004) disclose numerical simulations for IPTT interpretation.
Conventional analytical solution for multi-layer model in IPTT interpretation is based on the assumption that each layer is homogeneous and the drilled well is a vertical well. But in the real world, a layer may be characterized with different geological models, e.g., homogeneous or heterogeneous. And the drilled well can be vertical well or deviated well. In addition, conventional analytical solution for IPTT interpretation of a deviated well is based on the assumption that the model is one layer homogeneous model. Since the deduction of an analytical solution is very complicated, it is very difficult to extend this approach to situations of multi-layer deviated well or multi-layer dual-porosity well (vertical or deviated). On the other hand, the application of numerical simulation methods is more flexible and is able to handle the situations of multi-layer deviated well or multi-layer dual-porosity well (vertical or deviated). But the application of a numerical solution is very time consuming.